Where, \(c_{l}\)  and \(s_{l}\)  are constructed by stacking \({c}_{l}(t)\)  and \({s}_{l}(t)\)  at different time instances. The second non-convex term of (REF ) can be replaced with a convex surrogate [1]}.

\({^{k+1}}{\xi _{2,l}} = \min _{\xi _{2,l}}\Big ( \frac{1}{2}\xi _{2,l}^T\ddot{\textbf {P}}^{T}\ddot{\textbf {P}}\xi _{2,l}- \langle ^{k}\lambda _{\psi ,l},\xi _{2,l}\rangle \nonumber \\+ \frac{\rho }{2}\left\Vert \arctan 2({^{k+1}}s_{l},{^{k+1}}c_{l}) - \textbf {P}\xi _{2,l}\right\Vert _2^2 \Big ),~ \textbf {A}\xi _{2, l} = \textbf {b}_{\psi }\) 
